The sub-synchronous interactions (SSIs) observed in wind power plants have gained attention in recent years. These oscillations are characterised by the diversity of wind power generation types, power grids and power electronic devices. Two pure electrical oscillations, namely induction generator effect (IGE) and sub-synchronous control interaction in wind farms, are firstly discussed on their different characteristics. Particularly, IGE normally falls into the category of sub-synchronous resonance. Then two major types of wind turbines: doubly fed induction generator and permanent magnet synchronous generator with respect to their participations in SSI are reviewed according to the current research status. Several typical analysis and mitigation techniques in existing literature are also expounded in regard to their advantages and disadvantages. Additionally, the research on a grid-connected voltage-source converter in combination with the phase-locked loop, which has caused instability issues including SSI, is briefly introduced. Conclusions are drawn and several perspectives on the future work are presented at the end of this study.

In recent years, the subsynchronous oscillation (SSO), which occurs in direct-drive permanent magnetic synchronous generators (D-PMSGs)-based wind farm, has great impact on the stability of power system. The different parameters and operation conditions of D-PMSGs lead to the subsynchronous interaction (SSI) among D-PMSGs. What is more, the SSI will influence the SSO characteristics of the system of D-PMSGs-based wind farm integrated to AC network. Here, considering the difference of parameters or operation conditions among D-PMSGs in the wind farm, eigenvalue analysis, based on the small-signal state-space model of two aggregated D-PMSGs which are equivalent to wind farm, is carried out. Then the stability and the SSI between D-PMSGs of the equivalent system can be studied, and the dominant D-PMSG can be determined based on the participation factors. Lastly, the detailed electromagnetic transient simulation model of D-PMSGs equivalent system is built in PSCAD/EMTDC. The simulation is conducted to corroborate the eigenvalue analysis. The result shows that an obvious SSI exists between two aggregated D-PMSGs. Furthermore, the different SSO characteristics among D-PMSGs in the wind farm indicate the study of SSO problem based on an aggregated D-PMSGs model may leave out some useful information.

Generators connecting to a series compensated transmission system can be exposed to subsynchronous resonance (SSR) and require a comprehensive vulnerability assessment. This study presents an SSR assessment framework and tools to more efficiently assess all types of generation in a large system with multiple generators and meshed series capacitors. The developed framework covers torsional interaction, torque amplification, and induction generator effect/control interaction and includes three assessment stages: topology screening, frequency scan, and detailed electromagnetic transient study. Topology screening based on max-flow min-cut theorem is applied to identify the set of transmission outages forming radial connections between generators and series capacitors. Frequency scan analysis is then conducted to further analyse the SSR vulnerability with all the possible combinations of transmission outages identified in the topology screening results. Nearby generators are modelled by frequency-dependent impedance tables, which consider the equivalent impedance looking into the generators over the range of 1–120 Hz. An electromagnetic transient simulation will be required to confirm the SSR vulnerability identified in the frequency scan analysis. The developed framework and tools have successfully been applied to a large power system with multiple series compensated circuits to ensure reliable generation interconnection and operation.

For doubly fed induction generator (DFIG)-based wind farms, the occurrence of sub-synchronous oscillation (SSO) is detrimental to the system operation and should be suppressed promptly. A low-cost control strategy based on reactive power regulation of DFIG-based wind farm is proposed to suppress SSO. First, the influence of the reactive power output of wind farms on SSO is studied in the entire operating region of DFIGs, and several uncertainty factors are taken into account. Furthermore, a reactive power regulation-based control strategy is proposed to suppress SSO by changing the operating point of the system. In addition, a PASTd (Projection Approximation Subspace Tracking based on the Deflation Technique)-based identification method is utilised to realise the online SSO monitoring. The implementation of the proposed control strategy is low cost since it does not require any additional supplementary equipment. The time-domain simulation results have also verified the effectiveness and strong robustness of the proposed control strategy.

The deployment of more and more power electronic devices results in the sub-synchronous oscillation caused by sub/super-synchronous harmonics associated with inverter-based renewable power generators (IRPGs). New measurement devices are needed to monitor the operation states of renewable power generator (RPG) areas. In this study, a synchronised measurement device for power systems with high penetration of IRPGs (SMD-R) is proposed and developed. Unlike traditional synchronised measurement devices, an SMD-R is able to perform real-time inter-harmonics and fundamental phasor estimation that are reported by different data frames in different rates by being installed inside a wind turbine or an integration station of RPG. The integration of SMD-R and the message format for inter-harmonics are outlined. A spectrum line curve fitting based algorithm is proposed to estimate inter-harmonics via a short data window. To track the dynamic process of RPG areas fast and precisely, an adaptive fundamental phasor algorithm based on phasor parameter behaviours identification is developed. The proposed SMD-R is implemented in a CompactRIO of National Instruments. Experiment results verify the accuracy and effectiveness of the proposed device.

The existing phasor-measurement unit (PMU) and wide-area measurement system (WAMS) based on the fundamental synchrophasors are insufficient to accurately capture the dynamics of sub/super-synchronous resonance or oscillation (SSR/SSO). To address this issue, this study proposes a new method for the simultaneous and precise measurement of the fundamental and multiple sub/super-synchronous harmonic phasors. It improves the classic discrete Fourier transform (DFT)-based method by adding adaptive frequency detection, modal filtration and phasor correction and compensation. Thus, in the context of SSR/SSO, the phasors of both fundamental and interharmonic components can be precisely obtained at local PMUs and the control/data centre of WAMS. The basic procedures and the prototype implementation of the method have been elaborated, and the performance has been examined with simulation signals as well as the field data recorded from an actual SSO incident. The results have verified its high precision, noise immunity and fast response.

This study proposes a comprehensive PWM-based modular multilevel converter (MMC) model in both time and frequency domain at the same time. The time-domain model not only accelerates simulation speed but also describe the characteristics of sub-modules, such as the dynamic voltage-balancing process of sub-module capacitors. The frequency-domain model provides the output impedance of the grid-connected MMC inverter in positive-sequence and negative-sequence coordinates. The proposed model, validated by results of different scenarios listed, at last, predicts and eliminates sub-synchronous/super-synchronous oscillations with impedance shaping method.

The impedance-based analysis is widely used to study stability problem between wind turbine system and grid network. Stationary sequence domain impedance has advantages over synchronous dq domain impedance due to its easy measurement in practical application. However, there is frequency coupling effect in sequence domain impedance, and a 2×2 impedance matrix is needed which makes the system be multiple-input–multiple-output system, which makes stability study and controller tuning much more complex compared with single-input–single-output (SISO) system. In this study, impedance model of doubly fed induction generator (DFIG) in sequence domain considering frequency coupling effect is derived based on the complex vector modelling method, which can obtain the straightforward block diagram representation of DFIG impedance. On the basis of the proposed model, the interaction of DFIG and different kinds of grid impedances are studied. Gershgorin theorem is applied to study the fidelity of SISO impedance model in stability analysis. Finally, the proposed impedance-based analysis is verified through simulation.

Impedance analysis has been widely used in small-signal stability analysis of power systems and power electronic device. This study proposes an iterative approach to impedance model of individual device. The proposed method applies numerical iteration in the calculation of impedance model instead of complex mathematical derivation. It is easy to be implemented in computer programs. First, initial value of a key impedance/admittance of the target device is set. Second, an iterative algorithm is designed according to structure of the device and transfer functions of its components. Finally, the equivalent impedance is computed and stability characteristics of the whole system are analysed. The obtained model could include all elements of the target device, such as phase-locked loop and shaft system. Thus, it could also be applied to the analysis of sub-synchronous control interaction and torsional interaction. The proposed method could provide impedance contribution from different parts of the target device. This character will benefit the analysis and solution of system instability.

For three-phase LCL-type inverter connected to weak grid, the bandwidth and dynamics of phase-locked loop (PLL) directly affect small-signal perturbation modelling, which causes the control dq frame of PLL being no longer aligned with the system dq frame of weak grid. Thus, considering the effect of PLL, a small-signal perturbation admittance model is firstly built. Secondly, by the rotating matrix, variables in the system dq frame are transformed into the control dq frame. Then, the interaction between two dq frames is established based on an admittance model in consideration of the PLL, and the inverter output admittance is obtained. Finally, the effect of PLL, grid impedance and LCL-type filter parameters on system stability are analysed. As a conclusion, with an increase in PLL bandwidth and grid impedance, the system stability gradually is decreased, even resulting in the system instability. In addition, the larger the active damping coefficient is, the better the system stability is. While, the increase of filter capacitance and grid-side inductance leads to the decrease of system stability. The conclusions have certain guiding significance and reference value for the design and safe operation of three-phase LCL-type grid-connected inverter. The simulation and experiment verify the validity of theoretical analysis.

In the conventional power systems, the synchronous generators (SGs) are known to suffer stability issues under weak grid conditions. Recently, similar problems are observed in the inverter interfaced systems, including the full voltage source converter (VSC)-based high-voltage DC, and partial VSC interfaced doubly fed induction generator (DFIG) systems, but the root causes of these instabilities in reality are not completely understood yet. This study aims to provide a possible unified explanation for the origin of these instability issues. With the experiences of SG's instability mechanism, for the VSC and DFIG systems, the dynamics of outer power flow controls are mainly focused, and the reduced-order models are parallelly presented first. Then, centralised around the active power control loops of these systems for analysis, it is found that an open-loop zero will move to the right half plane with grid strength decrease. The borders for the occurrence of right-half-plane zeros (RHPZs) are analytically derived. Further, a general interpretation regarding these identified RHPZs’ limitations, including the adverse phase lag effect on stability and the attraction effect on the stability boundary, is illustrated. In addition, a uniform explanation for the origin of the RHPZs in these systems is also provided. Time-domain simulations are conducted to validate the analysis.

This study presents the impact of the doubly fed induction generator (DFIG) with power system stabiliser (PSS) on critical low-frequency oscillations (LFOs) caused by the synchronous generators (SGs). These LFOs arise due to uncertainties in a system such as generating/loading conditions, intermittent wind power and may cause instability. To improve the stability, the PSS is added. This study studies the effect of varying wind speed, DFIG locations and its capacity with and without PSS on stability. The system is analysed by replacing SGs with DFIG. The sensitivity analysis is carried out with wind power penetration and voltage gain as sensitivity parameters. This identifies electromechanical modes of oscillations that have positive and negative impacts on the system. The transient and small-signal stability (SSS) investigations are done using non-linear simulation and eigenvalue analysis, respectively. The system uncertainties are modelled using inverse output additive perturbation structure to elude the mathematical difficulty. The location and selection of best local input signals for PSS are evaluated from residue method and time-domain simulation analysis. The effectiveness and robustness of the proposed approaches are verified on IEEE 9-bus test system. The PSS improves the transient stability and SSS of the system.

This study focused on the use of the non-dominated sorting genetic algorithm (NSGA-II) to achieve an optimal power system stabiliser (PSS) parameters for a given operating point with a renewable source of energy so as to increase the system damping and guarantee enough stability margin. The parameters tuning was formulated using an eigenvalue-based multi-objective function. In recent years, the changeability and fluctuation of the wind power injected into the network have led to new challenges in small signal stability (SSS). These wind speed change and load demand change perturbations take place routinely and cause the variation of the operating conditions. However, as the conventional PSS is conceived for a fixed operating point in order to obtain the linearised transfer function model, it cannot yield good results when the operating range is too wide. To this end, the adaptive neuro-fuzzy inference system was proposed to estimate the stabiliser parameters in real time after a learning phase. The nine-bus Western System Coordinating Council and the obtained simulations results were assessed using Matlab/Simulink package. The validity of the proposed methodology was checked through the PSS parameters evolution simulation for daily load forecast curves and monthly wind speed prediction curves.

Several studies have reported the improvement of system stability with a doubly-fed induction generator (DFIG) based wind turbines. Due to the remote location of DFIG, the local signals measured may not contain the complete oscillation information of the power system. This study describes an optimisation enabled wide area damping control (WADC) for DFIG to mitigate both local and inter area oscillations. Wide area measurement systems (WAMSs) which include phasor measurement units and synchrophasors are used for a centralised controller for damping inter-area and local oscillatory modes. The proposed damping controller parameters are optimised along with the local power system stabiliser settings for maximising the impact on system modal damping. The challenging shortcoming of WAMS based controller is the variable communication latency which can adversely affect the controller if not accounted in the controller design process. The proposed WADC algorithm addresses this issue and compensates for the delayed and time stamped error signals. The variable latencies are normalised in the optimisation algorithm in the design of controller parameters. The proposed algorithm is verified with transient simulation in PSCAD/EMTDC for the most severe three-phase faults. A set of comprehensive case studies are performed to analyse the effectiveness of the proposed algorithm for the noisy, delayed communication signals.

With regards to the problems in which the power-oscillation characteristics of power systems with high penetration of renewable power generation are complex and difficult to effectively analyse, a novel network virtual-inertia method is proposed to evaluate the power oscillation in such systems. Firstly, the network virtual inertia is defined and developed. Secondly, the network virtual inertia is calculated and obtained based on the measurement information. Thirdly, the relationship between the network virtual inertia and generator inertia is constructed. Finally, the network virtual inertia of power systems with high penetration of renewable power generation is analysed. The evaluation method is effective and easy to implement. Simulations involving four-generator two-area containing renewable power generation were conducted under various disturbances to prove the effectiveness of the proposed method.

Modular multilevel converter (MMC) based dc system has become an effective solution for renewable energy integration and power transmission. However, the converters based on power electronic devices have no significant inertia characteristics. This study presents an inertia emulation and dynamic voltage support scheme for MMC-based dc systems. The proposed scheme enables the converter to contribute an inertial response to the interconnected ac network by varying the sub-module (SM) capacitor voltage. Meanwhile dc system voltage can be kept to the rating or a permitted range by dynamically adjusting the number of SMs switched on according to the variation of capacitor voltage. The implementation and different stages of the proposed scheme are discussed. The inertia support ability of the scheme is also investigated. Simulations under various power disturbances on PSCAD/EMTDC are given to demonstrate the feasibility and advantages of the proposed scheme.

This study proposes a modified virtual inertial control (MVIC) scheme for doubly-fed induction generator (DFIG)-based wind turbines (WTs), which both improves the frequency response of these renewable resources and enhances the power system oscillation damping capabilities. It is shown that the proposed control structure enables the WT to participate prudentially in system frequency regulation, which means the amount of WT kinetic energy released to the grid and its participation in system frequency support is alleviated as its stored energy decreases. The proposed control strategy is introduced conceptually, and its performance is verified analytically. Effects of wind speed variations on the small-signal stability of DFIG WTs equipped with the proposed MVIC is investigated, as well. For these purposes, the system characteristic equation and its damping ratio, as well as the transfer function between the wind speed and the wind turbine rotor speed are derived and analysed. Eventually, time-domain simulation results and modal analysis verify the performance of the proposed method and demonstrate its superiority as compared to the conventional virtual inertial controllers.

For unbalanced three-phase grid voltage, the traditional Virtual Synchronous Generator (VSG) control cannot overcome the distortion of output current. For this reason, a new control method is proposed in this study. The additional positive-sequence current adjuster to the traditional VSG control allows the reference current to track the positive-sequence current, and inhibit the negative-sequence components. Meanwhile, the oscillations in the power system are decreased. The proposed method has been simulated using Matlab/Simulink and verified experimentally on actual platform. The reliability and effectiveness of the proposed control method have also been compared with the traditional VSG control.

Wave energy is one of the electric generation options based on renewable energies, especially suitable for islands due to the energy resource availability and the higher energy cost of energy in its electric grids. The oscillating nature of the wave resource is prone to produce negative impacts in these electric grids when considering scenarios of high penetration of wave energy generation. This study analyses the impact of wave energy generation on the power system frequency for the particular case study of Tenerife Island (Spain). Then, hourly data related to sea states in Tenerife, during a whole year, will be provided to generate an electric power profile, based on a model of a wave energy farm with a specific wave converter type. A previously developed dynamic simulation model of the Tenerife transmission network will be fed with these power profiles and the hourly electric generation and consumption profiles to analyse the system frequency. A complete set of analysis during the whole year will be accomplished in order to determine the number of over-frequency events according to the grid codes. Finally, some corrective measures will be proposed as conclusions, e.g. energy storage devices, as the most reliable solution to mitigate frequency deviations.

In this study, the authors represent a modelling to analyse and simulate renewable power generation for two area power systems in the presence of high penetrated wind farm. The performance of assumed power systems may hazard without appropriate frequency amelioration methodologies. To complete the LFC model for two area power systems, the combination of automatic generation control and automatic voltage regulation of thermal units is considered. Due to the decline in the total inertia of power system associated with wind farm contribution, the self-tuning and adaptive fuzzy-based PID droop can be proposed in the structure of wind turbines instead of the fixed/traditional PID droop in de-loaded area to ameliorate the frequency excursions. Besides, the artificial bee colony algorithm can tune the parameters of membership functions for input and output signals based on a multi-objective function (MOF). The proposed strategy control is proved to be accurately stable under various load changes and yields more satisfactory performance in comparison to the conventional PID droop. This research generally includes wind farm collaboration in the frequency control by inertia, primary and secondary frequency control.

Power quality is a vital issue in distribution systems. Power quality issues have become important for the extensive use of sensitive equipment and integration of renewable generation. Several researchers have proposed for voltage sag mitigation devices to minimise financial losses arising from voltage sag. Augmentation of micro-level units like housing complex, super-specialty hospitals, rapid urbanisation has opened up demand for electricity. Modernisation in life has led to coextensive requirement for good quality power. Importance of micro-level consumers is to be considered while looking into the matter of optimal selection of voltage sag mitigation devices. In this study, a new framework is proposed for optimal selection of voltage sag mitigation devices to minimise voltage sag occurrence in a distribution system based on Nested Logit model. Nested Logit model has the essential characteristic for selection of optimal option by allowing equal preference to all the available customers’ choice. This model gives unbiased and equal importance to all the available mitigation devices. The optimal selection of mitigation devices is obtained using aggregate forecasting. Voltage sag severity index is used for placement of optimally selected voltage sag mitigation device. Two case studies are described to validate the proposed approach.

The occurrence of ferroresonances, due to the presence of voltage transformers in isolated-neutral in medium-voltage (MV) distribution grids, results in overvoltages and overcurrents that may damage the connected equipment. To prevent this phenomenon, the protection windings of the MV transformers have to be properly loaded for damping purposes. Mitigation equipment based on resistors, passive/active circuits and static converters have been proposed in the literature. This study proposes a new variety of mitigation equipment based on very simple power electronic converters operated as configurable resistor emulators. The proposed approach is evaluated theoretically and validated experimentally. A resistor emulator proof of concept is designed and applied for damping ferroresonances due to the occurrence of line-to-ground faults in isolated-neutral MV distribution power systems.

Power quality events associated with the occurrence of ferroresonances in medium voltage (MV) isolated-neutral distribution power systems are well known but they still happen in nowadays grids. This work deals with the study of ferroresonance events in a distribution grid region characterised by having distributed generators and being lightly loaded. The study shows that well-known solutions, i.e. voltage transformer damping, are difficult to apply due to the legal considerations and, alternatively, the distribution system operator can take actions to minimise their effect on the distribution system. The data provided and the obtained results correspond to a three-year measurement campaign at a real MV isolated-neutral distribution power system. The measurements and analysis given allow reaching general conclusions about the distribution system operation oriented to minimise the effect of ferroresonances.